Method for producing denture parts or for tooth restoration using electronic dental representations

ABSTRACT

The invention relates to a method for producing denture parts or for tooth restoration. According to said method, to reconstruct a tooth requiring repair or a defective condition, at least some of the missing exterior surfaces of denture parts or tooth restorations are adapted to the existing residual tooth material and/or the opposing teeth and/or the position of the neighbouring tooth and/or the occlusion position, by means of the optimisation of a generic dental-model data record of the desired tooth type, thus varying the linear factors of at least the most important components, (determined from the electronic data records of a larger number of measured tooth surfaces by primary axis analysis methods), in such a way that the selected optimisation criteria are fulfilled by the minimisation of an error function. After the successful adaptation of said surfaces to the residual occlusion position and the completion of the data record, the reconstructed denture part or the reconstructed tooth restoration is machine-manufactured.

The present invention relates to a method of producing a general,three-dimensional electronic image of a tooth and a method of producingtooth models, dental prosthetic items, or of making restorations ofdefective teeth or defective dental prosthetic items.

Various options are available for treating dental defects. One option isthe direct application of filling material in the mouth, ie the dentistremoves the decay and fills the hole with a filling material during thesame sitting. This approach is selected mainly for smaller defects. Forlarger defects, materials such as metal or ceramics, etc, are preferred,which cannot be fabricated directly in the mouth. In addition, in thecase of larger defects, configuring the occlusal surface in the mouth ismore problematic and difficult to carry out. Therefore, after preparingthe tooth, an impression is taken by the dentist. This impression issent to a dental laboratory and a plaster model is created. By takingaccount of the opposing teeth and, if appropriate, the jaw movements inthe form of articulators, it is then possible to produce the appropriatetooth restoration or dental prosthetic item. The aforementioned can be,for example, inlays, onlays, partial crowns, crowns, bridges, telescopecrowns, partial prostheses, etc. Needless to say, making a restorationof this type is very expensive. After the impression has been taken andthe plaster model created with alignment with the opposing jaw, waxingor sintering, embedding, casting or pressing, machining, fitting, andpolishing are carried out. The large number of steps and the limitedtechnical facilities in the dental laboratory have the result, on theone hand, that processing errors can occur and the quality of thematerial in the finished product may not be optimal, and, on the otherhand, that not all materials can be processed (eg, heavy-duty ceramics).In addition, the high cost of labor also results in great expense.

Recently, CAD/CAM technology has been viewed as an alternative toconventional production methods, in which the dental restorations anddental prosthetic items are produced with the aid of computer methods.In simple terms, the process involved is made up of:

-   1. Three-dimensional data acquisition of the preparation, or    multiple preparations.-   2. Generating a CAD data set of the tooth restoration, ie, designing    or computing the shell and/or interactive modeling of the shell on    the screen.-   3. Machining the finished CAD data set in a computer-controlled    milling or grinding machine (eg, CNC) or rapid prototyping systems.

The advantage of a method of this type is obvious:

-   1. Cost savings through automation and therefore time savings.-   2. The use of materials that are available in industry. These can be    sintered, cast, etc, in more optimal conditions than are present in    the laboratory and therefore have better material characteristics.    These advantages have already been exhaustively investigated,    specifically for ceramics and titanium.-   3. A denture is produced having consistent quality. No fluctuations    as a result of processing errors arise, as is the case with    conventional production processes.-   4. Entirely new materials such as zirconium oxide ceramics etc, that    hitherto could not be processed at all using the conventional dental    process or only at great expense can be fabricated using the CNC    method.

Some systems are already in use. A current survey can be found by way ofexample in a Number of ZWP (December 2001, Mehl). Furthermore, thePatent Specifications U.S. Pat. No. 5,217,375, EP 0643948, EP 0634150,EP 0913130 A2, and WO 0239056 describe systems of this type orindividual aspects of systems of this type.

One problem that has not yet been solved is production using thegreatest possible degree of automation of dental restorations thatalready have an occlusal surface, that satisfy all the functional andmorphological criteria of an occlusal surface, and that can be optimallyadjusted to the state of the opposing teeth.

In most systems, it is currently only possible to manufacture dentalframeworks. Similar to the conventional approach, in which, for example,a metal framework is filled out with ceramics or plastics material (thisapplies also to other materials such as special ceramics or plasticsframeworks), the basic framework is generated in the CAD/CAM process andsubsequently at least parts of the occlusal surface and other missingexterior surfaces are conventionally filled in using ceramics,composites, etc. These frameworks can be produced, eg, in the CADsoftware (design software) by enlarging the preparation or computing asurface, which lies at a specific, selectable distance (equal to thelayer thickness of the frame) from the preparation surface. In addition,it is also possible to include “convexities” and “deformations”. EP0913130 A2 in FIG. 13b discloses an approach of this type. EP 06 43 948A1 describes another example.

No method is yet available for the automatic generation of an occlusalsurface that is configured in accordance with all the desirable criteriaand requirements for a good tooth restoration or dental prosthetic item.However, this is especially desirable because in this way the usefulnessand cost efficiency of a CAD/CAM system would be increased and, aboveall, the CAD/CAM technology could be established on a large scale indentistry. At the same time, this method would also have to make itpossible to produce the computed dental prosthetic items in a machine.

Various methods for shaping an occlusal surface are described in theliterature and in patent specifications. For the reconstruction of inlaysurfaces, both linear methods as well as various extrapolation methodsare described (Mattiola, A., Mörmann, W. H., and Lutz, F,“Computerunterstützte Okklusion von Cerec 2 Inlays und Overlays”(Computer-supported Occlusion of Cerec 2 Inlays and Overlays) Schweiz.Monatssch. Zahnmed. 105: 12831290 (1995); Kunzlemann, K. H., Mehl, A.,Pelka, M.: “Automatische Rekonstruktion von Kauflächencomputergenerierter Restaurationen” (Automated Reconstruction ofOcclusal Surfaces of Computer-Generated Restorations) Zahnärtzl.Welt/Rundschau 102, 695703 (1993)). In the linear method, oppositepoints on the cavity border (usually in the oro-vestibular direction)are joined simply by a straight line and thus the defect is filled in.In extrapolation, the gradient of the still existing remaining toothstructure is continued into the defect, and thus the surface isreconstructed. It is obvious that this approach can only approximatelyyield a result resembling an occlusal surface. It is not possible toinclude morphological criteria or the condition of the opposing teeth.At the same time, this method is only suitable for relatively smalldefects.

A second option lies in further three-dimensional optical scanningeither of the existing occlusal surface, before the tooth is ground, orof an occlusal surface that is modeled individually using wax orplastics material (eg, Mattiola, A., Mörmann, W. H., and Lutz, F.,“Computerunterstützte Okklusion von Cerec 2 Inlays und Overlays”(Computer-Supported Occlusion of Cerec 2 Inlays and Overlays) Schweiz.Monatssch. Zahnmed. 105: 12831290 (1995), Mehl, A., Gloger, W., Hickel,R., “Erzeugung von CAD-Datensätzen für Inlays und Kronen mitfunktionellen Kauflächen” (Creating CAD Data sets For Inlays and CrownsHaving Functional Occlusal Surfaces) Deutsch Zahnärztl. line 52, 520524(1997)). By clicking on or selecting reference points on the adjacentteeth, the scanned preparation and the scanned occlusal surface can bepositioned relatively to each other, and the entire restoration can bebuilt up. In this case, however, a wax model must be produced manually,which means that the automation advantages of using the CAD/CAM systemare no longer afforded. In most cases, when treating a tooth, theinitial occlusal surface will not be usable due to existing decaydefects or insufficient pretreatment, so that this option remainsrestricted to a limited area of applicability. A further option ispresented in WO 0239056. This describes a patient archiving system, eg,a chip card for the patient, which contains stored dental records. Thesedental data can then be used at a later time when prostheses aremanufactured for the patient, and they can serve for reconstructing thedefect. In any case, it is assured that the built-up occlusal surface isoptimally adjusted to the gnathological system both morphologically andfunctionally. But, using these methods, corresponding long waiting timesmust be expected, so that for the treatment of a large population othermethods must currently be considered.

Other options involving the inclusion of occlusal surface geometries inthe CAD/CAM process are described in the following inventions. DE 198 38239 A1 describes groups of blanks for dental restorations, which can beassigned to various tooth types and whose external geometries aredetermined for the specific tooth types from average values that arederived from the relevant textbooks. However, this does not involve amathematical description of tooth surfaces that can be used for theCAD/CAM reconstruction of tooth restorations, but rather concerns anapproximate maximum-minimum estimate for the rough exterior mass ofmolded blanks, from which the desired individual tooth restoration canbe milled. In addition, the average values that can be taken from theliterature are only the length, width, or similar linear measurements,which cannot even approximately describe an occlusal surface for thecomputer-supported reconstruction process.

DE 199 23 978 A1 discloses a method of the computer-supported,patient-specific representation and planning of dental and/or dentalprosthetic work, in which a digitized image database is generated usinga multiplicity of model tooth and jaw views, the model views includinghealthy objects and those with disease findings, eg, individual teeth.Such an image database contains images of typical mouth regions. Thismethod functions as a computer-supported expert system for arriving atdiagnoses and treatment schedules in dental work. For thethree-dimensional reconstruction of tooth defects, such as is necessaryin the CAD/CAM process for producing dental prostheses, this method isnot appropriate because patient-specific findings do not suffice forprecise individual adaptation of the image databases. The image databaseis only designed to make available typical standard forms for discussingtreatment schedules with the patient, and modification by combiningthese data to form a new representative data set is not attempted.

EP 06 43 948 A1 discloses a method of producing a dental restoration, inwhich a self-learning data library of basic tooth forms is used. In thiscontext, the method limits itself to producing crown frameworks andprovides for only learning such parameters as layer thickness, thelocalization and thickness of convexities, and the approximate course ofthe preparation line. This simple “learning” does not lead tomathematical or parametric descriptions of tooth surfaces that aresuitable for the reconstruction of individual tooth defects having acomplete external geometry such as anatomically and functionally shapedinlays, onlays, crowns, and bridges. In particular, this method does notmake it possible to take into account the adjacent remaining dentitioncondition, such as of adjacent teeth and opposing teeth. Furthermore, inthis case the shape provided by nature is not imitated, but rather onlythe physical design parameters of structures are generated as a functionof the experience of the dental technician or expert.

U.S. Pat. No. 5,257,203 discloses a method of producing a dentalrestoration, in which a database of standardized generic tooth shapes isused, these generic tooth shapes typically being computer-basedrepresentations of standardized plaster models of teeth. The generictooth shapes used in this method are not tooth shapes that are derivedmathematically or logarithmically from a database and therefore are notgeneric tooth models as described in the sense of the present invention,but rather are standardized plaster models that are only scannedthree-dimensionally, and this data set is used for reconstructionpurposes. The disadvantage is here again that no generally valid designprinciple underlies the standardization, and shaping depends only on themanual dexterity and the experience of individual experts with aresulting limitation of the multiplicity of shapes that arise in nature.

A further option for producing tooth restorations is described inSaliger, G., Designing a Cerec Crown, in Cerec 10 year AnniversarySymposium, ed. W. H. Mörmann, Quintessence, Chicago, 1996 or in DE19642247. Here the data set of a model tooth is adjusted and adapted tothe prepared tooth. Essentially, this model tooth is scaled, translated,and rotated according to the mesial-distal extension of the defect. Aresilient deformation can improve the result. Saliger, 1996 (see above),presents a subsequent interactive possibility of rotating andcontrolling the occlusal surface relatively to the opposing tooth. Inaddition, the cusps can be changed in their position. All this takesplace interactively. Finally, the tooth restoration is carried out bymachining.

The problem in all of the aforementioned procedures resides primarily inthe following facts:

-   -   Contact points with the opposing tooth are only subsequently        established, in that the adjustment is carried out through        interactive distribution or the model tooth is modified until        there is contact with the shell. This often results in shapes        that are completely atypical of teeth, because the model tooth        is from the start not optimally adjusted to the overall        situation.    -   There is no automated process for selecting the best model tooth        (in case more than one is available). Currently, that is only        accomplished on the basis of visual rules.    -   Working and making changes interactively at the monitor yield        effects that are difficult to imagine in three dimensions and        therefore those with minimal experience in computer work can        master this procedure only after a long period of practice and        daily use.    -   Neither the morphology of the adjacent teeth, or antagonists,        nor even the tooth type situated at an opposite position in the        same jaw is taken into account. In many cases, this is important        to ensure a harmonious incorporation of the restoration in the        jaw system.    -   Changes in the model tooth through scaling, cusp positioning,        and interactive deformations do not necessarily yield tooth-like        surfaces.    -   For all interactive or automated adjustments there does not yet        exist a method that guarantees that, following the modification,        an occlusal surface will result that is very similar to a        natural tooth. Since the criteria of a functionally and        statically good occlusal surface are not yet known to science        and have not even been demonstrated, the requirement for every        restoration must be that it approximates to the greatest extent        possible natural circumstances and forms, so as not to cause any        lasting damage to the teeth, the tissue, or the joint.

The aforementioned problems are overcome by the present invention, whichmakes possible the manufacture of tooth restorations, dental prostheticitems, or tooth models having occlusal surfaces and/or surfaces thatgreatly approximate a natural tooth and that are optimally integrated inthe jaw from functional and morphological points of view, with it beingpossible to automate the fabricating process to a greater extent, ie,with substantially fewer interactions and in an error-free, ie,user-friendlier manner.

In the present patent specification, dental prosthetic items areunderstood to be parts or the entirety of total or partial prostheses(eg, telescope prostheses, bracket prostheses, interim prostheses, etc)or implant structures, and tooth restorations are understood to bebridges, telescope crowns (primary and secondary parts), crowns, inlays,onlays, overlays, and partial crowns. Tooth models are used asprosthetic teeth, as independent models, as components used forpractice, training, and demonstration purposes or for depiction inelectronic or print media. To be distinguished therefrom is the conceptof the generic tooth model or generic tooth model data set, as will beexplained below.

On the one hand, the present invention creates a method of producing anelectronic data set of an average tooth that can be used for producing adental prosthetic item, a tooth restoration, or a tooth model, accordingto an example embodiment. In addition, the present invention alsocreates a method of producing an electronic data set of a generic toothmodel that can be used for building up a prosthetic item, a toothrestoration, or a tooth model, according to an example embodiment.Furthermore, the present invention indicates a method of producing toothmodels, dental prosthetic items, or tooth restorations, according to anexample embodiment. An example embodiment indicates a use of the methodof creating a three-dimensional electronic image of the average tooth,or of the method of producing an electronic data set of the generictooth model. An example embodiment indicates a use of a numericallycontrolled machine for producing tooth models, dental prosthetic items,or tooth restorations, which machine is controlled by a data set that isobtained in accordance with the present invention. Refinements of themethod according to the present invention are indicated in other exampleembodiments. Example embodiments indicate a device for visualizing,adjusting, and justifying a generic tooth model data set.

An electronic image of an average tooth as obtained according to thepresent invention, or the data set of a generic tooth model, isespecially well-suited as the starting point for producing a dentalprosthetic item, tooth restoration, or tooth model, because the averagetooth or, in more general terms, the generic tooth model data set isdetermined by real teeth, unlike a conventional electronic tooth model,which is based on the ideas of the author of the electronic tooth model,which possibly coincide more or less with nature.

For example, if a restoration for a defective tooth is produced with theassistance of an electronic average tooth, or generic tooth model, asobtained according to the present invention, the natural shape of thetooth that is expressed in the average tooth, or the generic toothmodel, takes precedence and not a tooth model derived from a person'sideas.

For example, in producing a tooth restoration, the average data set, orthe generic tooth model, obtained according to the present invention,can be taken as the starting point, and these data sets can be adjustedto the specific tooth being repaired, taking into consideration theremaining parts of the tooth surface of the defective tooth or theremaining dentition condition, in that these data sets are transformedby interactive interventions or by software-controlled automatic systemsso as to carry out the aforementioned adjustment to the remaining toothsurfaces of the tooth being repaired or of the remaining dentitioncondition adjacent the tooth being repaired.

Particularly good starting conditions are obtained for the generic toothmodel data set. On the basis of a correspondence analysis, a principalcomponent analysis and a linear combination are carried out in themanner described in these embodiments, from which a generic tooth modeldata set is produced. With the assistance of the generic tooth model, itis possible to establish the framework within which it is possible toadjust the model data set to the electronic image of the remainingstructure of the tooth to be repaired, without deviating from the supplyof natural tooth shapes. The generic tooth model data set can beadjusted to the defective part of the tooth being repaired in aninteractive manner or completely automatically using software controland processing. If a numerically controlled machine is controlled inaccordance with a data set that is obtained in this manner, the resultis a physical tooth part which approximates very well the appearance ofthe former intact surface of the tooth being repaired, and it ispossible to achieve this result in a way that is comparatively simplefor the dentist or dental technician.

The methods according to example embodiments are concerned with creatingone or at least very few generic tooth model data sets, or averageteeth, of a specific tooth type (eg, upper jaw No. 6, or even large,medium, and small upper jaw No. 6, etc). These surfaces provide adequatetooth-like reconstruction for a number of situations. Furthermore, thegeneric tooth model data set makes it possible that every modificationthat is carried out on this surface under specific criteria (see below)results with high probability in a natural occlusal surface, and thatall possible permitted variants of modifications describe the entiretyof virtually all of the tooth morphologies that arise in nature. In thiscontext, the number of adjustment variables is small, and thereconstruction of tooth surfaces can be automated.

In this context, this generic tooth model data set, or the average toothsurface are generated by the greatest possible number of data sets ofthe same tooth type. In general, the electronic data sets can be scannedboth two-dimensionally and three-dimensionally. Two-dimensional scanningis carried out, eg, by metric photography, and three-dimensionalscanning, eg, by white light strip projection, etc, stereophotogrammetric methods being also conceivable. However, for thereconstruction of defective teeth and defective dental prosthetic items,data sets are required that are scanned in at least three dimensions.Examples of tooth types are molars, premolars, cuspids, and front teeth.However, the tooth type can also be represented by “upper jaw No. 6”,“lower jaw No. 4”, or “upper jaw No. 1”, etc. Moreover, it is alsopossible to distinguish according to age and abrasion, sex, ethnicgroup, size of teeth, morphological peculiarities, etc, for example, thegroups “upper jaw No. 7 age 50-60 years”, “upper jaw No. 6 with andwithout tuberculum carabelli”, “lower jaw No. 3 in female persons”,classifications in large, medium, small No. 6, etc, can be examples of atooth type. It is also possible, eg, to combine adjacent teeth into one(combined) tooth type in order to integrate or to analyze theinterrelationships between adjacent teeth. Using the information of theadjacent tooth, it may be possible, for example, to select the toothsurface for the defective tooth or for the defective dental prostheticitem. The concept of tooth type therefore contains extremely variableclassification possibilities in accordance with the task at hand, whichshould be kept in mind when considering the generality expressed in thepatent claims.

For a specific tooth type, the respective data sets must, in a firststep, be referenced to each other (brought into the same coordinatesystem and have approximately the same orientation), and between thesurface points of one data set correspondences must be found to those inthe other data sets. These correspondences occur, eg, between prominentpoints and structures of the surface. This assignment can be carried outmanually, and it can be carried out by searching for and assigningspecific characteristic features, distinctive structures (cusp shape,fissure pattern, marginal ridge, etc). In this regard, it is preferableto select a process that automatically locates these correspondencepoints and/or structures, since up to now no proven metricallyascertainable states exist that actually comprise the prominent points,structures, or characteristics of a specific tooth type. On thecontrary, to date there does not exist in the entire professional dentalliterature any reference to even an approximately mathematicaldescription of tooth surfaces that would be in any way suitable for theCAD/CAM process.

As a possible implementation option, the following method has proven tobe feasible: First, the data sets of the scanned tooth surfaces of aspecific tooth type are brought into the same coordinate system in orderto obtain the best possible starting point for the automaticdetermination of correspondence points. This can be carried out usingmatching routines by minimizing the distance error function, in thatrotation and translation parameters are measured. After the coordinatetransformation has been completed, the correspondence analysis iscarried out. From image processing, it is possible here to successfullyapply modified algorithms to the optical flow. Furthermore, through theresilient registration, or matching, of specific features (fissures,cusp tips, cusp overhangs, and marginal ridges) between the individualtooth surfaces, it is possible to create correspondences and to locateimaging prescriptions. Finally, the assignment of many points throughcorrespondences among all data sets is achieved.

More precisely, this is specified below with reference to the method ofoptical flow. The starting point is m library tooth surfaces of aspecific tooth type, taken from a tooth library, in the form z_(j)(x,y), where j=1, . . . m as scanning data. Also permissible are parametricrepresentations z_(j)(u, v), where u=u(x, y) and v=v(x, y), where, forexample, these can be polar coordinates, etc. Any complicated threedimensional surfaces having undercutting can be approximated piece bypiece using the above functions. In a wider sense, descriptions of teethinvolving any number of dimensions are permitted for other methods.

Starting from a reference tooth z_(j)(x, y), where Rε{1, . . . ,m},using a correspondence analysis for each point of the reference tooth,the corresponding point on the occlusal surface z_(j)(x, y) is searchedfor. This can take place also by linking correspondences in sequence, inthat, beginning from one tooth, the correspondence to a further tooth isestablished, and from this new tooth a further correspondence to a thirdtooth, and so on. In addition, before every new correspondencedetermination, a new average tooth can be computed from the availablecorrespondences and can serve as the starting point for the newcorrespondence analysis. Overall, this can be achieved using analgorithm that automatically locates these correspondences withoutrequiring prior knowledge, according to an example embodiment. Onepossibility is the method of optical flow (for any 3-D objects otherpossibilities are described in Shelton, C.R.: 3-D Correspondence.Master's thesis, Massachusetts Institute of Technology, 1998). Theresult obtained is for each tooth z_(j)(x, y) is a correspondingtwo-dimensional vector field {right arrow over (v)}_(j)(x, y) where

${{\overset{\rightarrow}{v}}_{j}\left( {x,y} \right)} = \begin{pmatrix}{\Delta\;{x_{j}\left( {x,y} \right)}} \\{\Delta\;{y_{j}\left( {x,y} \right)}}\end{pmatrix}$so that for each coordinate pair (x, y) of the reference tooth z_(R)(x,y), the corresponding point of the tooth z_(j)(x′, y′) is generated fromthe relation:z _(j)(x+Δx _(j)(x, y), y+Δy _(j)(x, y)).

With respect to tooth surfaces, it is expedient, in addition to thesmoothness of the displacement field relative to the z-coordinates, toalso require smoothness with respect to the gradients, because gradientsalso represent an essential feature of the occlusal surfaces.Furthermore, using the correspondence analysis approach, one can alsoattempt, after finding each new correspondence, to merge this data setwith the existing corresponding data sets and to search therein for anew linear combination which approximates to the greatest extentpossible the next data set, which is not yet in correspondence. This newlinear combination can then be used in the automatic correspondencesearch process. Thus, in an iterative manner, all data sets can bebrought into correspondence.

Since not all the points of a surface can be clearly assigned to thepoints of another surface, it is possible to require that thedisplacement field behave graphically like a resilient diaphragm, thisbeing virtually non-displaceable between the unambiguouscorrespondences, whereas in between, ie, in the areas of unclear or weakcorrespondences, it can relax quite freely. This can be computed, forexample, by minimizing an energy function that arises from coupling ofmany springs between the individual surface points (approximation forthe continuous resilient diaphragm).

One interesting expansion for the computation of the optical flow liesin the fact that, in addition to the three-dimensional datarepresentation z(x, y), other criteria or surface descriptions areconsulted for the correspondence analysis, as is indicated in an exampleembodiment. For example, this could be the gradient field of the toothsurface. Better than height data, gradients describe specific featuressuch as edges, corners, or more pronounced changes in the surface. Bycreating a new feature vector {right arrow over (m)} where

$\overset{\rightarrow}{m} = \begin{pmatrix}{z\left( {x,y} \right)} \\{\nabla{x\left( {x,y} \right)}}\end{pmatrix}$and introducing a new standard for this feature space:∥{right arrow over (m)}∥² =z ²(x, y)+β(∇z(x, y))²in which β establishes the weighting of the gradient field in relationto the relief image, the displacement field {right arrow over (v)}(x,y)=(Δx(x, y), Δy(x, y))^(T) for the feature vector {right arrow over(m)} can be computed by analogy to the above, if the standards ∥{rightarrow over (m)}_(x)∥ and ∥{right arrow over (m)}_(y)∥², and therespective scalar products <{right arrow over (m)}_(x), {right arrowover (m)}_(y)> and <{right arrow over (m)}_(x), Δ{right arrow over (m)}>are used. Of course, it is also possible to conceive multidimensionalfeature vectors, by taking into account further characteristics of thetooth surface. These could be, for example, texture values, curvatures,etc. The weighting factor β (or other weighting factors) make itpossible to establish the specific influence of the individual featurefields. All of these measures yield a powerful tool, which, for thetooth surfaces, makes possible an automatic analysis of correspondencesthat does not require prior knowledge.

When these correspondences have been located, the reference tooth, in anext step, can be represented as a vector in 3n-dimensional space (inthis context, n equals the number of selected points that lie on thetooth surface), ideally an equidistant grid will be used, and thetypical number of points can go from 10,000-200,000):{right arrow over (D)} _(R)=(x ₁ , y ₁ , z _(R)(x ₁ , y ₁), x ₂ , y ₂ ,z _(R)(x ₂ , y ₂), . . . , x _(n) , y _(n) , z _(R)(x _(n) , y _(n)))In a consistent manner then, proceeding from the reference tooth (orfrom the linear combination) and from the corresponding vector field v_(j)(x, y), all other teeth of the library are represented as3n-dimensional vectors:{right arrow over (D)} _(j)=(x ₁ +Δx _(j)(x ₁ , y ₁), y ₁ +Δy _(j)(x ₁ ,y ₁), z _(j)(x ₁ +Δx _(j)+(x ₁ , y ₁,), y ₁ +Δy _(j)(x ₁ , y ₁)),x ₂ +Δx _(j)(x ₂ , y ₂),y ₂ +Δy _(j)(x ₂ , y ₂), z _(j)(x ₂ +Δx _(j)+(x₂ , y ₂,), y ₂ +Δy _(j)(x ₁ , y ₂)),x _(n) +Δx _(j)(x _(n) , y _(n)), y _(n) +Δy _(j)(x _(n) , y _(n)), z_(j)(x _(n) +Δx _(j)÷(x _(n) , y _(n),), y _(n) +Δy _(j)(x _(n) , y_(n))))

In this way, the same vector coordinates, ie, indices, also representthe corresponding points, specifically between all teeth. All of the mvectors, which correspond to the m library teeth, span a space that isdesignated as the tooth space for the corresponding tooth type.Therefore, it is now possible to compute the average tooth {right arrowover (D)} from the individual transformed library teeth {right arrowover (D)}_(j):

$\overset{\rightarrow}{D} = {\frac{1}{m} \cdot {\sum\limits_{j = 1}^{m}\;{\overset{\rightarrow}{D}}_{j}}}$

At this point, it is possible to use the new average tooth as areference tooth, start the above process once again, and repeat it manytimes. In this way, the average tooth can be determined even moregenerally. Or various reference teeth are taken and the result issubsequently averaged. In an example embodiment, this average data setis made available as an average tooth of a specific tooth group (toothtype) (FIG. 9).

If the individual tooth surfaces are present as vectors, it is possible,with a high degree of probability, to represent each additional tooth{right arrow over (Z)} as a linear combination of the existing teeth:

$\overset{\rightarrow}{Z} \approx {\sum\limits_{j = 1}^{m}{\beta_{j} \cdot \;{\overset{\rightarrow}{D}}_{j}}}$

A principal component analysis is available for reducing the number oflinear factors β_(i) and of teeth {right arrow over (D)}_(j). Since eachtooth type is recognizable to the person skilled in the art throughspecific features, those components should have great influence as aresult of the principal component transformation in characterizing thespecific features of the tooth type. Thus, a sufficient description ofmost tooth surfaces is obtained using the linear combination of part ofthe principal component. This principal component analysis can bedirectly carried out on the tooth data {right arrow over (D)}_(j), asindicated in an example embodiment. The implemented portion p of theresulting principal components (usually those that contribute most tothe variance) are linked mathematically by a linear combination (linearfactors a_(i) and principal components {right arrow over (P)}_(i)) asfollows:

$\begin{matrix}{\overset{\rightarrow}{Z} \approx {\sum\limits_{i = 1}^{p}{a_{i} \cdot \;{{\overset{\rightarrow}{P}}_{i}.}}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

As indicated in an example embodiment, before the principal componentanalysis is carried out with respect to the tooth vectors, it ispossible to displace the vector space such that the average value 0 isgenerated. This is obtained by carrying out a subtraction operationbetween the individual tooth vectors and the average tooth. Thedifferential vectors that are generated can then be analyzed also usingprincipal component methods. Overall, using these methods involving onlya few variable parameters, an adequately efficient description of newtooth forms is achieved, which can be represented as linear combinationsof these new parameters (linear factors) and principal components. Thedecisive advantage is that, as the parameters change, one of theexisting natural tooth data will be approximated with a high degree ofprobability. Therefore, the restoration to be created will be verytooth-like, and the risk of obtaining bad occlusal surfaces iseliminated.

In what follows, the principal component analysis is described ingreater detail with respect to the tooth vectors for the case in whichthe average tooth is subtracted, ie, the vector space of the teeth isdisplaced such that the average value 0 is generated. Therefore, evenafter the principal component analysis, the average values of theprincipal components (eigenvectors) are 0. From each tooth vector {rightarrow over (D)}_(j), the average tooth {right arrow over (D)} issubtracted, and a new differential vector {right arrow over (Δ)}_(j) isgenerated, where{right arrow over (Δ)}_(j) ={right arrow over (D)} _(j) −{right arrowover (D)}.

The principal component analysis then supplies the eigenvalues λ_(k)with their associated principal axes (principal components,eigenvectors) {right arrow over (P)}_(k) where k=1, . . . m. Thefollowing characteristics are produced:

-   1. Eigenvalues λ_(k) correspond to the variances in the direction of    the principal component {right arrow over (P)}_(k).-   2. The sum of eigenvalues λ_(k) corresponds to the sum of the    variances of {right arrow over (Δ)}_(j), ie, the total variance of    {right arrow over (Δ)}_(j). Since an average displacement has no    influence on the variance of the values, the sum of eigenvalues    λ_(k) therefore corresponds to total variance of {right arrow over    (D)}_(j).-   3. The proportion of a principal component {right arrow over    (P)}_(k) of the total variance of the data sets is given by:

$\lambda_{k}/{\sum\limits_{l = 1}^{m}\;\lambda_{l}}$

-   4. The proportion of the first p principal components {right arrow    over (P)}_(k) of the total variance is by analogy given by:

$\sum\limits_{l = 1}^{p}\;{\lambda_{l}/{\sum\limits_{l = 1}^{m}\;\lambda_{l}}}$

For example, in the case of upper molars it is found that the first 7principal components describe approximately 70% of the total variance of170 teeth.

A large proportion of all possible tooth surfaces {right arrow over (Z)}can now be relatively precisely approximated using a linear combinationof the first p principal components {right arrow over (P)}_(k) (α_(i)being the linear factors):

$\begin{matrix}{\overset{\rightarrow}{Z} \approx {\overset{\rightarrow}{D} + {\sum\limits_{l = 1}^{p}\;{\alpha_{l} \cdot {\overset{\rightarrow}{P}}_{l}}}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

If reasonable limiting conditions are placed on parameters α_(i),(Equation 1) and α_(i) (Equation 2) (eg, that the new tooth be locatedwithin the space encompassed by the existing teeth or be situated atleast not very far from it), any linear combination will describe atooth in accordance with (Equation 1) or (Equation 2). A tooth data set,which is usually generated by a linear combination of principalcomponents and, if appropriate, by the addition of an average tooth, isdesignated in this patent specification as a generic tooth model dataset, or a generic tooth model, with respect to the tooth type ofinterest. Synonymous therewith, and in an abstract sense, the generictooth model data set, or the generic tooth model, is conceived in thispatent specification with respect to the tooth type of interest as acombination of data sets of the selected principal components and, ifappropriate, of the average tooth. This combination can be conceivedeither physically, eg, as individual data sets that are joined by linksor by references, or by merging the same to form one large data set. Ifa representation of this generic tooth model, or generic tooth modeldata set, is desired, it is only necessary to multiply the speciallinear factors with the principal components and, if appropriate, to addthe average tooth. The generic tooth model, or the generic tooth modeldata set (hereinafter abbreviated as “generic tooth” in some instances),therefore represents a kind of mathematical description of the overalltooth space of the corresponding tooth type.

According to example embodiments, the reconstruction process for thedefective tooth or the defective dental prosthetic item can be carriedout using the average tooth, or the generic tooth model, and can also besubstantially automated. Reconstruction signifies the build up or atleast partial repair of the missing shell of the defective tooth or ofthe defective dental prosthetic item. The defective tooth can be aninlay, onlay, overlay, partial crown, crown, bridge preparations, etc,and the defective dental prosthetic item can concern filling out regionsof missing teeth, eg, intermediate bridge members, implant structures,or parts of partial prostheses or total prostheses. The concept ofremaining dentition condition in this patent specification designatesthe scanned information (in particular, data sets) of the prepared toothor teeth (the tooth or defective teeth) or of the defective dentalprosthetic item, and the additional optional inclusion of scannedinformation of the remaining tooth structure, the opposing jaw, thefunctional and static/occlusal bite registration, the adjacenttooth/teeth and/or the gum component, or the alveolar ridge. The conceptof opposing jaw signifies generally only the inclusion of one or moreopposing teeth, ie, the tooth or teeth that are opposite the defectivetooth or the defective dental prosthetic item. The concept of opposingtooth is synonymous with the technical term antagonist. However, in thispatent specification, the term opposing tooth also includes part of theopposing jaw or the entire opposing jaw. If, from the relevantpreparation or defective dental prosthetic item and from the surroundingremaining dentition condition, specific construction points, orcorrespondence points, or correspondence structures are selected, eg,cusp tips or marginal ridge points on the remaining tooth structureand/or possible contact points with the opposing tooth or adjacent tooth(FIGS. 9 to 11), then, assuming knowledge of the relevant correspondencepoints and structures on the generic tooth model, average tooth, etc,the reconstruction can best be carried out using optimization processes.On the average tooth, rotation, translation, scaling, and, optionallyaffine transformation parameters are usually generated usingminimization processes. In the case of the generic tooth, there isadditional optimized adjustment of the parameters (linear factors) ofthe principal components such that insertion of the generic tooth, afterit has been modified in accordance with the parameters, takes place inan optimal manner. Optionally, it is also possible to build into thisprocess secondary conditions such as limiting the magnitude of theparameters, so that the result does not lie far beyond the tooth space,or the condition that the opposing occlusal surface or functional biteregistration should not be penetrated, although it may rest upon thecontact points. It is also possible to take into account qualityparameters such as minimal layer thicknesses for a material or a surfacedesign having optimal load bearing properties.

In addition to the individual correspondence points, however, it is alsopossible to locate in their totality all existing remaining toothsurfaces (eg, in the case of inlays, onlays, partial crowns), oralternatively corresponding structures, ie, specific characteristicareas and shapes, and to take all the points of these remaining toothsurfaces and/or structures into the correspondence. This can be carriedout, eg, by analogy to the above, using the method of optical flow.Another possibility is to use matching by optimizing the parameterscorresponding to a quality function (eg, distance function). In thiscontext, it is again decisive that the tooth be not deformed in anymanner but rather remain along the principal components and thereforewithin the range of the shape of natural teeth.

In general, the generic occlusal surfaces and data sets of the defectivedental prosthetic item or of the defective tooth do not lie in the samecoordinate system. Therefore, in the generic occlusal surface, inaddition to the parameters along the principal components (linearfactors), at least rotation and translation must also be determined. Itis also possible to include scaling, but this is not entirely advisablein this case because this factor should already have been integrated inthe principal component representation. One possibility of solving theproblem lies in carrying out the adjustment process in two steps:

-   1. Rotation and translation of the average tooth into the coordinate    system of the defective tooth on the basis of correspondence points    and/or remaining tooth structure. This can be carried out, eg, using    the algorithm according to Umeyama (Umeyama, S.: Least-squares    estimation of transformation parameters between two point patterns,    IEEE PAMI 13(4); 276280, 1991), the scaling factor being set at 1.-   2. Improving the adjustment of the correspondence points by    optimizing the principal component parameters (if appropriate,    supplemented by the linear factors of rotation and translation,    etc).

The advantage is that direct solutions can be employed for both steps.In the general case (also a one-step solution), it is of course alsopossible to use familiar nonlinear iterative solutions (eg, gradientdecline methods, Levenberg Marquardt, etc).

If the original data set of the remaining tooth structure and/orcorrespondence points has been translated and rotated into thecoordinate system of the average tooth, then, on the basis of thecharacteristics of the generic tooth surface, optimal initial conditionsexist for the reconstruction of tooth surfaces. The objective lies indetermining the parameters (linear factors) such that the linearcombination (ie, a new occlusal surface) that results is adapted to theexisting situation to the greatest extent possible. This isaccomplished, eg, by minimizing an error function.

The adjustment can be further optimized by permitting only those linearcombinations which show a high degree of probability, ie, that giveprecedence to the most typical tooth shapes for the tooth space. In thisway, the result should lie, with great probability, within the convexshell of the tooth data. Alternatively, it is conceivable in thisconnection to include probability theory observations. The followingconditions should be taken into account:

-   a) The desired occlusal surface within the space of the tooth    surfaces should have the greatest possible probability, ie, its    shape should be the most typical possible for an occlusal surface.-   b) The measured points may have measuring errors (eg, as a result of    measurement or by mouse clicking). In order that a measuring or    processing error will not be excessively weighted in the selection    of the occlusal surface, here too a probability will be taken into    account for a measuring point as a function of noise or error    sources.

An approach of this kind could lead to the following maximization ofprobability:

${{P\left( {{\overset{\rightarrow}{c}\left. {\overset{\rightarrow}{z}}_{real} \right)} = {{{const} \cdot {P\left( {\overset{\rightarrow}{z}}_{real} \right.}}\overset{\rightarrow}{c}}} \right)} \cdot {P\left( \overset{\rightarrow}{c} \right)}}\mspace{95mu} = {{const} \cdot {\mathbb{e}}^{{- \frac{1}{2\pi^{2}}}{{{M\overset{\rightarrow}{c}} - {\overset{\rightarrow}{z}}_{real}}}^{2}} \cdot {\mathbb{e}}^{{- \frac{1}{2}}{\overset{\rightarrow}{c}}^{2}}}$

This probability is maximized if the quality function E is minimal:

$E = {{{{{M\overset{\rightarrow}{c}} - {\overset{\rightarrow}{z}}_{real}}}^{2} + {\gamma \cdot {\overset{\rightarrow}{c}}^{2}}} = \min}$$\gamma = \frac{1}{\sigma^{2}}$ where${z = {{\sum\limits_{l = 1}^{p}\;{\lambda_{l}c_{l}{\overset{\rightarrow}{p}}_{l}}} = {M\overset{\rightarrow}{c}}}},$where the matrix M=(λ₁{right arrow over (p)}₁, λ₂{right arrow over(p)}₂, . . . , λ_(p){right arrow over (p)}_(p)), and the measuring errorhas a variance of σ² The measured optimal generic tooth surface is veryeasy to integrate into the given remaining dentition condition. Theremaining dentition condition is the scanned information (in particular,data sets) of the prepared tooth, including remaining tooth structure,opposing jaw, functional and static bite registration, adjacent teethand/or gum line and alveolar ridge. Undoubtedly, even smallerdifferences will generally be found, such as small steps or gaps in thetransition to the remaining tooth structure, excessively elevated pointsthat penetrate the bite registration or the adjacent tooth, contactpoints that are still missing, etc. In addition, under certaincircumstances, surfaces that are still missing such as approximalsurfaces, oral and vestibular surfaces can be built up. These processesthat are in toto designated as adjustments, which generally involve onlyslight changes, then supply the finished data set that is used forcontrolling a machine.

In an example embodiment, the use of these computed data sets isdescribed for the physical production process. In principle, allpossible automated production methods can be used such as CNC milling orgrinding, laser processing, stereo lithography, or lithographicsintering methods. The material spectrum for the tooth restoration,dental prosthetic items, or tooth models can range from plasticsmaterials to metals (titanium, gold, steel, etc) to ceramics. Indentistry, a series of materials are currently specially available forthe CAD/CAM process.

An example embodiment defines the entire production process fromscanning to fabrication. Implementation variants as indicated above canbe used here by analogy. From the description and the drawings, a personskilled in the art can derive further variants that are not indicatedhere in detail, so that they can also be regarded as being fullyincorporated in this patent specification.

An example embodiment explicitly relates to taking into accountfunctional and/or static or bite registrations. One great advantage ofthe entire occlusal surface adaptation using mathematical and electronicmethods lies in the fact that it is no longer necessary to go throughthe entire production chain from taking an impression of the opposingjaw, making a plaster model of this opposing jaw, articulating theopposing jaw and assigning to the sawed model or preparation model, downto determining and justifying the jaw joint parameters, etc. Thealternative here represents direct modeling of the opposing jaw positionby taking bite registrations in the mouth. The static bite registration,sometimes also known as an occlusal bite registration, is obtained byplacing molding material at the desired location, the patient thenbiting down and leaving the teeth in the bite-down position until thematerial sets. Information regarding jaw movements is obtained by thepatient also carrying out the greatest possible number of different jawmovements before the impression material has set. This then generatesthe functional bite registration, sometimes also termed the FGP(functional generated path). Using this approach, very precise,three-dimensional information is obtained regarding the pathways of theteeth opposite the preparation, and therefore also borderlines anddesign indications as to where contact points may lie, and where thereconstructed tooth surface should not be expanded, ie, where thehighest points might be. According to an example embodiment, it isprecisely this information that is consulted for determiningcorrespondence and therefore for more precise adaptation of the averagetooth, or the generic tooth. Using appropriate mathematicalformulations, this information can be included in the optimization orminimization methods in the form of limiting conditions. This conditioncould be as follows: Contact points are points (interpolation of thepoint having a secondary derivation equal to 0) that contact the biteregistration, whereas the remaining areas of the reconstructed surfacemay not be contacted.

An example embodiment describes the possibility of automating theprocess of locating the contact point with the opposite tooth(antagonist). By comparing the static (occlusal) bite registration withthe functional bite registration, both of which were taken from thepatient for the corresponding situation as indicated above and arelocated (referenced) as measured data sets in the same coordinatesystem, the areas in which the one bite registration is at a shortdistance from the other bite registration, or where they contact eachother, are especially well displayed. These areas represent the possiblecandidates for contact with the antagonists, and no contact lines willbe found in the other areas. If it is known where the correspondingcontact points are located on the generic tooth surface, or on theaverage tooth, then it is possible to automate the optimization of thelinear factors to a substantial extent.

According to an example embodiment, for the approximal surfaceconfiguration (eg, position of the approximal contact, extension, etc)and for the selection of the correspondence points or structures (eg,marginal ridges, shapes of the occlusal surface, etc) the scannedinformation of the adjacent teeth is also included. Similarly,individual points (eg, contact points) or the shape and structures ofthe opposing tooth can be used for the creation of correspondence, andthus the selection of the best fitting tooth surface can be carried outfor the reconstruction of the defective tooth or the defective dentalprosthetic item. Similarly, information on the corresponding,symmetrically opposite tooth could be taken into account, because it isoften presupposed that these tooth shapes are only mirror images showinggreat resemblance to each other. In particular, this example embodimentincludes the possibility of drawing conclusions concerning the shell tobe built up or at least parts of this shell, from the informationconcerning the adjacent tooth/teeth on the basis of the interrelationsthat are found, from the principal component analysis or correspondenceanalysis, to exist between adjacent teeth of the same patient (eg, forcreating the generic tooth model of adjacent teeth). One possibilitylies in optimizing the parameters of the combined generic tooth modeldata set when adapting to the adjacent tooth/teeth, while at the sametime modifying the tooth surface to be reconstructed, to an appropriateextent. The same method can be used for the opposing tooth, or thesymmetrically opposite tooth. In particular, this example embodimentmakes reference to the fact that the information regarding adjacenttooth/teeth, opposing tooth and/or symmetrically opposite tooth/teethcan also consist of two-dimensionally scanned data sets. Based on thesedata sets, it is possible to form conclusions concerning thethree-dimensional structure with the assistance of a correspondinggeneric tooth model through the optimization of imaging, illuminating,rendering, and/or projecting functions (eg, see Blanz, V., Romdhani, S.:Face Identification across Different Poses and Illuminations with a 3-DMorphable Model. Proc. Int. Conference on Automatic Face and GestureRecognition, 202-207, 2002) and to use them for the reconstruction. Theadvantage of this two-dimensional scanning lies in the fact that imagesor data sets can be created relatively easily, eg, using an intraoralcamera or photographic equipment on the patient.

An example embodiment indicates that necessary adjustments can still becarried out if undesirable areas and irregularities are still presentafter computing the best-fitting generic tooth, or average tooth. Suchfeatures may comprise small steps or gaps in the transition regionleading to the remaining tooth structure, points that are too elevatedand penetrate the bite registration or the adjacent tooth, contactpoints that are still missing, etc. For this purpose, methods areavailable that ensure that the modifications remain locally delimitedand as small as possible, whilst at the same time producing a harmoniousand smooth transition to the unmodified regions. This can be carried outusing familiar deformation and/or morphing methods. In addition, undercertain circumstances, the missing surface parts such as approximalsurfaces, oral and vestibular surfaces can be built up. Possible methodsof automatically building up these surfaces are described below. All ofthese processes can be carried out automatically or interactively. Ininteractive manipulation, the dentist or dental technician can stilloptimize the configuration in accordance with his or her ideas. Usually,this possibility should always be implemented in methods for producingdental prosthetic items or tooth restorations.

With the assistance of the generic tooth, various occlusal andfunctional concepts can be realized. In dentistry there are varioustheories about where the static and functional contact lines to theadjacent tooth or antagonist are to be found. The generic tooth providesthe opportunity to decide, quasi online, which concept is to bepreferred and where the contact lines should be (FIGS. 9-11). In thiscontext, for example, the desired contact lines are marked on thegeneric tooth, the corresponding correspondence points on the biteregistration and/or the remaining tooth structure or adjacent tooth, asindicated in an example embodiment either once and for all for aspecific user or laboratory favoring a specific concept, oralternatively before each new treatment. By adjusting the parameterswith regard to the corresponding points, a functionally configurednatural occlusal surface is obtained after the minimization methods havebeen employed. This method functions only when using generic teeth,because in the case of tooth libraries, the best tooth can only beselected if, due to changes in the contact/functional situation, thecorresponding reference points of all teeth have to be determined anew,which is an expensive undertaking, given the large number of teeth. Onthe other hand, in the case of deformation of only one model tooth notcreated on the basis of a generic tooth and in cases where if theprincipal component analysis has not been carried out, there can be noassurance that the work will produce a harmonious, tooth-like result.

Example embodiments describe a method of producing dental prostheticitems, which, proceeding on the basis of 3-D data sets of the opposingjaw situation (FIG. 2) and the preparation (FIG. 1) or multiplepreparations, which are referenced to each other, are created in thatthe most fitting occlusal surface is automatically selected from a toothlibrary (FIG. 5) after referencing the existing bite registration to thepreparation data sets on the basis of the possible overlapping areas(FIG. 3), following the selection of the most appropriate correspondencepoints (FIG. 4). An error minimization method of the selection andadaptation of a library occlusal surface that is very well-suited forthis purpose and does not proceed in an interactive manner is described,eg, in Umeyama (Umeyama, S.: Least Squares Estimation of TransformationParameters between Two Point Patterns. IEEE PAMI 13(4): 276280, 1991).Subsequently, existing interferences or overcuttings relative to theopposing tooth row and/or adjacent teeth are eliminated, and in the caseof inlays, onlays, and any partial crowns, the remaining tooth structureis also taken into account, the missing exterior surfaces are built up(FIGS. 6 and 8), and they are then adjusted to the preparation line suchthat a virtually smooth, harmonious transition is achieved (FIG. 7). Byfusing the exterior and interior surfaces along the preparation line(marginal curve), the dental prosthetic items can then be machined. Thefirst decisive factor is that in comparison with the above-mentioned,familiar methods, as a result of selecting many different teeth from atooth library, it is not the tooth that is adjusted to this situationbut rather a tooth is selected that is already very well adapted to thissituation, in which it is then only necessary to carry out very smalladjustments, which are therefore less error prone and easier toautomate. The second advantage is the separation of important orcomplicated parts of the tooth surface from less important or simplerparts. The former involves, eg, the occlusal surface, and the latterconcerns the vestibular, approximal, and oral surfaces of the teeth. Asa result of this division, it is possible to restrict oneself to betteradaptation of the more complicated surfaces obtained from the toothlibrary, while the exterior surfaces are automatically built up andreconstructed. For the exterior surfaces, it is sufficient to indicateonly a few construction points (FIGS. 8 and 16). One implementationpossibility is the computation of Bezier, NURBS, or B-spline surfaces,which adjoin continuously and smoothly the corresponding parts of thepreparation limit and the border of the integrated library data set andthat interpolate the construction points (such as approximal contact orconvexities of the vestibular or oral surfaces). An example embodimentspecifies this method.

An example embodiment specifies how this tooth library can be set up. Inthis context, it is expedient to have a structure in which a data set,which contains the type and the features that are to be taken intoaccount for the selection, is assigned to each tooth data set eitherthrough referencing or through being given an appropriate name. Inaddition, a library is designed to be made up of tooth surfaces thatderive from natural, cavity-free, and intact teeth.

The most general form of a tooth library contains the entirety of allpossible tooth shapes that arise either naturally or artificially. Thetooth library is sensibly divided into groups of different tooth types.This subdivision in accordance with tooth type can involve, for example,molars, premolars, cuspids, and front teeth. Alternatively, the type canbe designated as upper jaw No. 6, lower jaw No. 4, upper jaw No. 1, etc.Furthermore, it is also possible to distinguish according to age andabrasion, gender, ethnic group, size of teeth, morphologicalpeculiarities, etc; for example, “upper jaw No. 7 age 50-60 years”,“upper jaw No. 6 with and without Tuberculum Carabelli”, and “lower jawNo. 3 in females”, can represent examples of tooth types. The concepttooth type therefore includes extremely variable possibilities forclassification depending on the task at hand.

An example embodiment describes a method in which, in creating thegeneric tooth model data set, the factor of age or degree of abrasion istaken into account, the tooth library surfaces of a specific tooth typebeing available in all ages or degrees of abrasion, and the obtainedcombinations of linear factors and principal components that describethis factor are used in order to optimally adjust the abrasion for therespective remaining dentition condition.

An example embodiment depicts a new way of creating tooth restorations,in which a suggestion for the possible localizations of all contactpoints with the opposing tooth/teeth (ie, the contact points with theopposing jaw) is determined automatically. For this purpose, afunctional bite registration and a static or occlusal bite registrationare scanned, and the data sets are referenced in the same coordinatesystem, so that this system corresponds to the situation in the patientor in the model, and subsequently all areas or points that are at a veryshort distance from one registration to the other are filtered out. Thedecisive factor is that no contact points can or should be found outsidethese areas. Therefore, even the configuration of the contact points canbe automated or at least substantially simplified.

An example embodiment describes a method in which the data sets of theaverage tooth, the generic tooth data set, the reconstructed dentalprosthetic items, the tooth restorations, or the tooth models areprepared for the production process by smoothing (filtering) or byspecial adjustment of the tool or processing geometries. This alsoincludes corrections of the milling machine radius, etc.

All the indicated methods are equally appropriate for inlays, onlays,partial crowns, crowns, and bridges. A further advantage, as indicatedin an example embodiment, lies in the fact that, on the basis of thereconstructed occlusal surface, it is also possible to achieve a reducedocclusal surface configuration for tooth frameworks, which ensures thatthe tooth veneer subsequently has an approximately constant layerthickness. This can be achieved by computing the new surface at aconstant distance from the reconstructed surface, or by shifting theocclusal surface toward the prepared tooth in accordance with thedesired layer thickness, at least by flattening out the area of thecusps and fissures.

An example embodiment describes the use of a numerically controlledmachine, by means of which, controlled by the data sets found, toothmodels, tooth restorations, and dental prosthetic items are physicallyproduced. In principle, all possible automated production methods can beused, such as CNC milling or grinding, laser treatment, stereolithography, or lithographic sintering methods. The range of materialsfor the tooth restoration, dental prosthetic items, or tooth models canextend from plastics materials to metals (titanium, gold, steel, etc) toceramics. In dentistry, a range of special materials is available forthe CAD/CAM process.

Example embodiments describe devices that make it possible, for thegeneric tooth model data set, to directly and interactively modify thelinear factors of at least the most important principal components usinga control device. At the same time, the effect of this change can beobserved and analyzed in a graphic display. In FIG. 18, one form of theconfiguration can be seen. The aforementioned devices can be used, eg,in place of automatic reconstruction and optimization, to providedentists or dental technicians with the possibility of adjusting thegeneric tooth model data set to the remaining tooth situationinteractively and in accordance with their own concepts.

Example embodiments describe possible methods that can be used to carryout the complete reconstruction of the occlusal surface without in theprocess explicitly cutting out remaining tooth structure or having tospecifically mark it. Rather, the complete data set of the defectivetooth is consulted (FIG. 12). By clicking on a few starting values(correspondence points) on the remaining tooth structure, a suggestionis offered, on the basis of which, for the further iteration oradaptation process, only those correspondence points are considered thatare located within a specific distance between the proposed toothsurface and the defective tooth (FIG. 12). The threshold of the distancecan also be varied or adjusted. In the reconstruction process,therefore, with a high degree of probability, points located in thecavity or on the ground areas of the tooth surface are not taken intoaccount, or they are not regarded as being significant due to the factthat they are present in small numbers. The advantage of this approachlies in the fact that, as indicated in example embodiments, it ispossible complete up the preparation line automatically. After theocclusal surface has been successfully reconstructed and adjusted, asearch is carried out for the areas in which a transition occurs fromsmaller distance values (areas where remaining tooth structure is stillto be found; here, generally, the reconstructed occlusal surface showsslight deviations) to areas having larger distances (areas where thetooth has been ground or tooth structure has been removed). Thepreparation limit or at least parts thereof must lie within thesetransition regions (FIG. 13). This approach can be improved if, in theseregions, the locations are sought having the greatest curvature on thesurface of the data set of the defective tooth, and these locations thathave the greatest curvature are joined in these regions to form a line(eg, FIGS. 14 and 15). In this way, it is possible to conceive a fullyautomatic process, from reconstruction to identification of thepreparation limit. However, it is also possible to advantageously usethis as support and for formulating suggestions for further interactiveprocessing by the user.

Example embodiments suggest an interactive possibility of inputting thepreparation limit. In this context, at specific distances, points areclicked on the surface of the electronic image of the defective tooth.This clicking can take place using various control and monitoringelements, eg, computer mouse, keyboard, joystick, or 3-D mouse. Aconnecting line in space is interpolated between the selected points. Inorder to obtain points from the scanned tooth surface, the connectingline is projected onto the surface (FIG. 14). In this context, it isdecisive that the direction of the projection can be selected forspecific sectional areas, or even for each section.

Example embodiments describe methods that make it possible to locate andto fill in any defective areas that arise in the data set of the toothrestoration or dental prosthetic items. Such defective areas can arise,for example, if the reconstructed occlusal surface, or the reconstructeddata set, does not cover the entire milled surface, or the adjustment inthe region of the preparation limit was not effected in an error-freefashion, and therefore the data set in this region spreads or has errors(FIGS. 6, 8, 15). Through an automatic comparison of the preparationline with the marginal curve of the reconstructed data set, it ispossible, by checking distances, to decide which regions of the lines orcurves are situated too far from each other and therefore requirefilling or buildup (FIG. 15). Since the starting points for thepreparation line and marginal curve do not have to be identical, thesections of the marginal curve of interest have to be automaticallyassigned to the corresponding sections of the preparation limit. Forcomputing the built up surface, it may also be necessary, within thetransitional region from one curve segment to another curve segment, toadd further points on the respective curves that previously, whenchecking the distance, could not be assigned to the area being built upand that now make it possible to produce the most continuous possibleline for computing the filled-in surface. An example embodimentexplicitly describes a method of closing these defective areas (see alsoFIG. 16).

The results can be monitored, and further necessary interactions thatshould be available to the dentist or dental technician can be madepossible for the operator by visualizing using 3-D glasses or 3-Dmonitors, etc. This is more familiar to the inexperienced operator.

When selecting the best occlusal surface, it is likewise possible toinclude the adjacent teeth, or antagonists, or the symmetricallyopposite tooth types, by means of the generic occlusal surfaces and theassociated principal components.

The present invention is presented in the description and in the Figuresonly by way of example on the basis of the exemplary embodiments and isnot limited thereto, but rather it includes all variations,modifications, substitutions, and combinations that a person skilled inthe art can derive from the present document, especially within thescope of the claims and the general representations as well as in thedescription of the exemplary embodiments and representations thereof inthe Figures, and that those skilled in the art can combine with theirexpertise and knowledge of the prior art, especially taking into accountthe complete disclosures of previous applications that are referred toin this description. In particular, all individual features andconfiguration possibilities can be combined.

IN THE DRAWINGS

FIG. 1 depicts a defective tooth;

FIG. 2 depicts a bite registration that is referenced to the defectivetooth;

FIG. 3 depicts the tooth according to FIG. 1 represented with adjacentteeth (top) and also with the referenced bite registration (bottom);

FIG. 4 is a representation of the tooth according to FIG. 1 showing abite registration and selected correspondence points;

FIG. 5 depicts a tooth surface selected from a tooth library on thebasis of the correspondence points;

FIG. 6 is a rotated representation of the item illustrated in FIG. 5having recognizable defective areas;

FIG. 7 depicts a fitted and completed tooth restoration;

FIG. 8 depicts a fitted tooth surface for a crown preparation with anindication of the interpolation points for the reconstruction of theexterior surfaces that are still missing;

FIG. 9 is an example of a generically generated tooth surface showingcorrespondence points;

FIG. 10 depicts a defective tooth having the correspondence pointsindicated in FIG. 9;

FIG. 11 depicts a defective tooth with bite registration and having thecorrespondence points according to FIG. 9;

FIG. 12 depicts an example for distinguishing the areas covering themilled tooth structure and requiring filling by a tooth restoration, andcovering the intact remaining tooth structure, on the basis of distancechecking during the process of reconstructing and adjusting the shell;

FIG. 13 depicts an example for detecting the preparation limit in thetransition region between the two previously distinguished areas;

FIG. 14 depicts an example of interactive marking of the preparationlimit in varying views and of projecting the connecting line onto thetooth surface;

FIG. 15 depicts an example of locating areas still requiring build-up bycomparison of the two marginal curves;

FIG. 16 depicts a complete tooth restoration in which the areas stillmissing have been automatically built up;

FIG. 17 depicts an example of a tooth restoration that has been carriedout in a machine in accordance with the generic tooth model method;

FIG. 18 depicts an example for a control device for modifying the linearfactors and simultaneously illustrating the modification;

FIG. 19 is a flow chart for the creation of an average data set or ageneric tooth model data set;

FIG. 20 depicts a flow chart for the reconstruction of a shell;

FIG. 21 depicts a continuation of the flow chart of FIG. 14 for thereconstruction of a shell;

FIG. 22 depicts a flow chart for the production of a dental prostheticitem or a tooth restoration; and

FIG. 23 is a flow chart for the production of a tooth model.

Further explanations will now be presented regarding the presentinvention and regarding the specific embodiments of the invention.

FIG. 1 depicts a three-dimensionally scanned defective tooth as a reliefdata set.

FIG. 2 depicts a bite registration referenced to a defective tooth. Thisbite registration contains information regarding the antagonist. Theregistration involved is either of a static bite registration and/or afunctional bite registration and/or the opposing tooth row. It is onlyimportant that this information be referenced in the same coordinatesystem as that of the tooth.

FIG. 3 depicts the same situation as in FIG. 2, but together with theadjacent teeth (top) and an additional bite registration (bottom). Theentire arrangement represents the remaining dentition condition. Theadjacent teeth, for example, provide information for the mesial-distalextension of the reconstructed external shell. In addition, on the basisof the shape of the adjacent teeth, which are significant for thereconstruction in the corresponding situation, it is possible to arriveat a selection for the tooth surface (shell).

In FIG. 4, by marking points on the remaining tooth surface and/orcontact points on the bite registration (opposing tooth row) and/or forapproximal contact with the adjacent tooth, the tooth surfaces can beoptimally adjusted either using a library tooth or using the generictooth with its principal components, through an appropriate minimizationof an error function. Instead of the spot markings, it is possible toselect larger areas, such as remaining tooth structure and/or contactsurfaces, on the basis of which the two surfaces can be adjusted bymatching or by optical flow. In a further embodiment of the presentinvention, localizations of possible contact points can automatically bedetermined by comparing the functional bite registration and the static(occlusal) bite registration.

FIG. 5 depicts an occlusal surface selected from the library andtransformed to the position, or a generic occlusal surface that isadapted to the situation by optimizing the linear factors of theprincipal components. In both cases, a relatively good result isobtained which must be adapted to the margins and to the opposing teethby deformation.

According to FIG. 6, an adjustment of occlusal surfaces in accordancewith still existing remaining tooth structure supplies missing gaps inthe area that lies mainly below the tooth equator. These gaps have yetto be closed. Although the selection of complete tooth surfaces (ie,including outer areas) would be possible, it is currently expedient toseparately adjust the occlusal surface and the exterior surface (oral,vestibular, and approximal surfaces). In this manner, parameters in theedge area are treated separately from parameters in the occlusal surfacearea, and therefore better adjustment is achieved in the individualareas. In addition, the process of completing the occlusal surfaces canbe carried out automatically as mentioned in the present invention.

According to FIG. 7, after adjustment to the edge/opposing tooth andafter buildup of the missing surfaces, the entire exterior contour(shell) of the tooth is obtained. The important factor here is theattainment of a smooth transition in the marginal regions. By combiningthis data set on the preparation limit with the data set of the scannedcavity/defect, the desired model is prepared for CNC processing andproduction in a machine.

FIG. 8. If no or little remaining tooth structure is available, or onlya small amount (eg, as in crown preparations), the missing exteriorsurfaces are built up over the entire circular area. In this context, itis expedient to indicate a few construction points. The build-up willusually run automatically. The other requirement is a smooth transitionin the marginal regions.

FIG. 9 depicts an example of a generically produced tooth surface. Inthis case, it is, say, an average tooth computed from 200 children'sintact first upper jaw molars No. 6.

FIGS. 10 and 11: The generic occlusal surface with its principalcomponents can in turn be adjusted to the remaining dentition conditionby implementing the remaining tooth structure (FIG. 10) and/or byselecting specific points on the bite registration (FIG. 11) and/oradjacent teeth, etc. In contrast to the direct use of a tooth library,it is possible, using the generic tooth model data set, to selectcontact points or contact structures or feature points or featurestructures immediately before the computation and design processes,since it is sufficient to mark these points on the generic tooth. In thetooth library, on the other hand, it would be necessary to provide eachindividual tooth with the new feature points. Therefore, this permits arapid change in accordance with the situation in order to realizevarious occlusion and shape concepts.

The invention claimed is:
 1. A method of creating an electronic data setof a natural looking tooth model for creating a dental prosthetic item,a tooth restoration, or a tooth model, said method comprising steps of:a) scanning a predetermined minimum number of teeth of a same tooth typeto provide a multiplicity of electronic data sets of the tooth type; b)for each individual electronic data set, assigning at least a certainnumber of at least one of correspondence points and correspondencestructures that are characterized for the tooth type in the individualelectronic data sets; c) performing a principal component analysis forat least one of the assigned correspondence points and correspondencestructures of the scanned teeth to generate principle components for thetooth type; and d) performing a linear combination of at least a portionof the resulting principal components for the tooth type of interest andmaking the linear combination available as a generic natural lookingtooth model data set, wherein at least one of steps a), b), c), and d)is performed by a computer.
 2. The method as defined in claim 1, whereinthe assigning of at least one of the correspondence points andcorrespondence structures is performed automatically.
 3. The method asdefined in claim 1, wherein, for the assigning of at least one of thecorrespondence points and correspondence structures, a weightedcombination is used taken from at least one of height values, gradients,and curvatures of corresponding electronic data.
 4. The method asdefined in claim 1, wherein the assigning of at least one of thecorrespondence points and correspondence structures is performedautomatically.
 5. The method as defined in claim 1, wherein, for theassigning of at least one of the correspondence points andcorrespondence structures, a weighted combination is used taken from atleast one of height values, gradients, and curvatures of thecorresponding electronic data.
 6. A method of using an electronicrepresentation of an average tooth or generic tooth model, as obtainedusing a method as defined in claim 1, as an electronic template for thecreation of physical tooth models, tooth restorations, or dentalprosthetic items using a machine that is controlled by the average dataset, or generic tooth model data set, or by parts of these data sets. 7.A method of creating physical dental prosthetic items or toothrestorations for defective teeth or for defective dental prostheticitems, using an electronic representation of an average tooth, orgeneric tooth model, as obtained using a method as defined in claim 1,said method comprising the steps of: a) carrying out a three-dimensionalscan of a preparation of the defective tooth or of a defective dentalprosthetic item, and creating an electronic data set representing thepreparation or defective dental prosthetic item; b) selecting at leastone of characteristic correspondence points and correspondencestructures from the electronic information of the scanned preparation,or of the scanned defective dental prosthetic item, for the tooth typeof the defective tooth, or for the tooth type appropriate to thedefective dental prosthetic item; c) assigning at least one of thecorrespondence points and the correspondence structures in theelectronic data sets of the scanned preparation or defective dentalprosthetic item in accordance with at least one of the correspondencepoints and correspondence structures in the data set of the averagetooth, or the generic tooth model; d) approximating at least one of thecorrespondence points and correspondence structures that are assigned toeach other to the greatest extent possible using an optimization method;e) making the data set obtained by the optimization the basis of thereconstruction of the missing part of the defective tooth, or forbuilding up the defective dental prosthetic item; and f) creating aphysical dental prosthetic item or a physical tooth restoration for thedefective tooth or for the defective dental prosthetic item using amachine that is controlled in accordance with the data set obtained instep e).
 8. A method for creating a three-dimensional electronic dataset of a generic tooth model, said method comprising steps of: a)generating a plurality of electronic data sets of a certain tooth typeby scanning a predetermined minimum number of teeth of a same toothtype; b) for each individual electronic data set, assigning at least acertain number of at least one of correspondence points andcorrespondence structures that are characterized for the tooth type inthe individual electronic data set, wherein the correspondence pointsand correspondence structures assigned for the individual electronicdata set identify correspondences between points and structures of theindividual electronic data set and points and structures of otherelectronic data sets, c) creating an average value from the electronicdata sets based on the assigning of the at least one of saidcorrespondence points and correspondence structures in each of theindividual electronic data sets; and d) making available an averageelectronic data set derived from said average value as an electronicrepresentation of a natural looking tooth having an average toothsurface with respect to the scanned teeth, wherein, after the assigningof at least one of the correspondence points and correspondencestructures, a plurality of difference data sets are created bysubtracting the average electronic data set from each of the electronicdata sets, and subsequently, a principal component analysis is performedfor the difference data sets, a linear combination of at least a portionof resulting principal components is performed for the tooth type, andthe linear combination is made available, together with the average dataset, as a generic tooth model data set, wherein at least one of stepsa), b), c), and d) is performed by a computer.
 9. The method as definedin claim 8, wherein the assigning of at least one of the correspondencepoints and correspondence structures is performed automatically.
 10. Themethod as defined in claim 8, wherein, for the assigning of at least oneof the correspondence points and correspondence structures, a weightedcombination is used taken from at least one of height values, gradients,and curvatures of corresponding electronic data.
 11. A method ofcreating an electronic data set of a natural looking tooth model forcreating a dental prosthetic item, a tooth restoration, or a toothmodel, said method comprising steps of: a) specifying a combination ofdifferent tooth types; b) scanning a predetermined minimum number ofteeth of a same combination of different tooth types to provide amultiplicity of electronic data sets of the specified combination; c)for each individual electronic data set, assigning at least a certainnumber of at least one of correspondence points and correspondencestructures that are characterized for the combination of different toothtypes in the individual electronic data sets; d) performing a principalcomponent analysis for at least one of the assigned correspondencepoints and correspondence structures of the scanned teeth to generateprinciple components for the combination of different tooth types; ande) performing a linear combination of at least a portion of theresulting principal components for the combination of different toothtypes and making the linear combination available as a generic naturallooking tooth model data set with a correlated combination of differenttooth types, wherein at least one of steps a), b), c), d), and e) isperformed by a computer.